Least-squares solutions to polynomial systems of equations with quantum annealing

  • Tyler H. ChangEmail author
  • Thomas C. H. Lux
  • Sai Sindhura Tipirneni


This work proposes and analyzes a methodology for finding least-squares solutions to the systems of polynomial equations. Systems of polynomial equations are ubiquitous in computational science, with major applications in machine learning and computer security (i.e., model fitting and integer factorization). The proposed methodology maps the squared-error function for a polynomial equation onto the Ising–Hamiltonian model, ensuring that the approximate solutions (by least squares) to real-world problems can be computed on a quantum annealer even when the exact solutions do not exist. Hamiltonians for integer factorization and polynomial systems of equations are implemented and analyzed for both logical optimality and physical practicality on modern quantum annealing hardware.


Least squares Quantum annealing Polynomial systems of equations Prime factorization Root finding 



The authors would like to thank Wu-chun Feng and Mohamed W. Hassan for their council and feedback. Also, the authors would like to acknowledge the anonymous reviewers for their helpful comments, which greatly improved this paper.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Tyler H. Chang
    • 1
    Email author
  • Thomas C. H. Lux
    • 1
  • Sai Sindhura Tipirneni
    • 1
  1. 1.Department of Computer ScienceVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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